I have tried to replicate this in 3.4.1 and 3.4.2 and I can not

BTW if i understand it correct #__content_frontpage has nothing to do with featured only with ordering

See: https://github.com/joomla/joomla-cms/blob/3.4.2/installation/sql/mysql/joomla.sql#L359-368

Ok, I'll show you:

The Featured article overview in back-end doesn't display Fetured items created from front-end:

The Article overview however shows the star:

When creating a menu item and showing the Featured articles in front-end, they won't show up.

For back-end part of saving Featured setting:
See https://github.com/joomla/joomla-cms/blob/3.4.2/administrator/components/com_content/models/article.php#L538-L545

For front-end part of saving Featured setting:
See https://github.com/joomla/joomla-cms/blob/3.4.2/components/com_content/models/form.php#L178-L195

When I add before form.php#L178-L195:

if (isset($data['featured'])) {
  $this>featured($data['id'], $data['featured']);
}

It works like it should. But maybe there's a better place to correct this.

Can you create a PR with your code proposal? Then it could be tested.
See https://docs.joomla.org/Using_the_Github_UI_to_Make_Pull_Requests if you don't know what a PR is

I have tried to produce this issue in joomla 3.4.1 but not able to produce it.
I can see the featured article in featured article view. please see the screen dump.

Dont know what to say - I have no problem or am I doing something different? Here is a video

https://www.dropbox.com/s/psh7hmep44144zf/featured.mp4?dl=0

I have watched this video and got the same output as per the video.

Thanks, for all the answers, that looks like the problem is not in Joomla itself. Excuse me for that, I have to look further into it. I think it's a plugin problem.

I shall close it at this time. If you do find it was a Joomla issue feel free to post here again and it can be re-opened